A framework is presented for visualizing and detecting climate variability and change based on time-dependent probability density functions (PDFs). The PDFs show how the distribution of values in the sample window changes over time and show more detail than do timeseries of windowed moments. A set of information-theoretic statistics based on the Shannon entropy and the Kullback-Leibler divergence (KLD) are defined to assess PDF complexity and temporal variability. The KLD-based measures quantify the representativeness of a 30-year sampling window of a larger climatic record: how well a long sample can predict a smaller samples PDF, and how well one 30-year sample matches a similar sample shifted in time. These information-theoretic statistics constitute a new type of climate variability, informatic variability. These techniques are applied to the Central England Temperature record, the longest continuous meteorological observational record.